The book by Alcock is aimed at students who (intend to) take up a mathematics degree course. They usually face the problem that there is a huge gap between school mathematics and university mathematics. Alcock’s book is not yet another ‘bridging course’ book. She wants to enable students to study effectively and efficiently by showing them what mathematical thinking is all about and what kind of study skills are important for successful mathematical studies. The first topic is addressed in the first part of the book which contains chapters on calculation procedures (partially familiar from school), abstract objects like numbers and functions, definitions, theorems, proof and proof types as well as on reading and writing mathematics. The second part is devoted to study skills. It treats lectures as a major learning arrangement, time management and dealing with other people and one’s own role. The book closes with a description of what mathematics lecturers do. The book can be highly recommended for beginning students because it demonstrates with many examples what mathematical thinking is all about. Being attacked by a ‘staccato’ of definitions, propositions, theorems, and proof sequences students often lose orientation and the book helps them to get a better sense of the thinking behind all the formal mathematics. It is also valuable for lecturers of beginner courses since it gives them hints on what to address explicitly in order to avoid students’ loss of orientation.

Reviewer:

Burkhard Alpers (Aalen)